In the thermodynamic limit \(V\rightarrow \infty \)  considered in the present
paper all intensive thermodynamical functions – \(P\) , \(n\) , \(s\) ,
and \(\varepsilon \)  –
depend on \(T\)  and \(\mu \) ,
rather than on the system volume \(V\) , see for instance
Ref. [1]}.
We start with the
GCE expressions \(\sum _iP^{\rm id}_i(T,\mu )\)  for the pressure \(P^{\rm id}(T,\mu )\) 
and particle number density \(n^{\rm id}(T,\mu )=\sum _in^{\rm id}_i(T,\mu )\) 
for the ideal
non-relativistic
quantum gas [2]}, [3]},
\(& P^{\rm id}_i=\frac{1}{3} g_i\int \frac{d {\bf p}}{(2\pi \hbar )^3}\frac{p^2}{m_i}\left[\exp \left( \frac{p^2}{2m_iT} -\frac{\mu }{T }\right) -\theta _i\right]^{-1},\\& n^{\rm id}_i=g_i\int \frac{d {\bf p}}{(2\pi \hbar )^3}\left[\exp \left( \frac{p^2}{2m_iT} -\frac{\mu }{T} \right) -\theta _i\right]^{-1}~,\) 
